The paper is a great overview on horn designs without bogging the discussion down with all the mathematical descriptions. It does over look the Tractrix contour and lenses, but does present a very interesting design. As you point out, something very doable by the average DIY’er. This is a definite read for the horn enthusiast and has my wheels grinding.

I think it does mention that tractix has more throat resonances because the walls are quite parallel at that point.

I can't figure out if it is ok for the horn to have a circular section rather than square i.e. could you just make a cone at the correct flare (with the proper transition arc at the driver) The square section is probably the easiest to make anyway.

Also, another price to pay for using this design other than efficiency is that it acoustically loads the driver unevenly. They claim that modern drivers aren't as sensitive to this as older designs. Anyone know if this is true? Does this mean that this design doesn't work well with direct drivers such as Lowther or Fostex full range?

Here is part of a Lynn Olsen article regarding horns, edge diffraction, and lining the mouth (of the horns-not your mouth! ) to eliminate it. Sounds l9ike one of the advantages of the tractix can also be taken care of with the lining. The Peavey lining might be thicker than 1/8" but appears to be recessed so the edge of the foam isn't protruding into the horn

".......From a technical standpoint, horn-loaded drivers typically have very low THD, IM, and FM distortion, uneven frequency response, reflections in the time domain, and very sharp cutoff characteristics at both ends of the frequency range. From the viewpoint of mainstream high-end designers, horns are beset by serious problems with impulse response, diffraction, and smooth dispersion.

The root of these problems, especially with cheaper PA-style horns, is the acoustic reflection from the edge of the horn-mouth. When a sound wave moves across a sharp boundary, it diffracts and re-radiates in all directions, like a separate driver located at the point of the reflection. The reflected wave from the horn-mouth then bounces back into the throat, which typically has a hard phase plug or a driver with a stiff cone. After it strikes that, it reflects right back outward again ... this succession of reflections is called a series reflection, and it is far more audible than the small ripples in the frequency response might indicate.

Although the frequency response doesn’t really indicate the full impact of the reflections, they show up in the impulse response or 3D waterfall display. (This is most clearly seen if the horn driver is measured without a crossover.) Inexpensive PA horns that are too short suffer most severely from this problem, and have the grossest "horn coloration" as a result.

There are solutions for this problem that work pretty well. If you can afford to lose 1 or 2dB or efficiency, you can line the inside of the horn with 1/8" wool felt. 1 to 3 inches extending from the lip of the mouth going inward will do the trick. The further you go back towards the throat, the better the damping, but if you overdo it, the bass response of the horn will start to droop, along with the efficiency. Think of it being like tweaking the VTA on your cartridge and you’ll be heading in the right direction. Of course, if you have access to a MLSSA or similar FFT system, you can adjust the impulse response to taste, as well as compensate the crossover accordingly. (Note: if you’re modifying a commercial horn, don’t forget to remove the wire mesh bug screen in the throat. The wire mesh creates a very unpleasant gritty harshness at levels above 90dB, and is only required for severe outdoor environments.)

The best solution is to eliminate the mouth reflection entirely. This has already been done with the Tractrix horn profile, invented by P.G.A.H. Voight in the late Twenties!

The Tractrix still has a sharp edge at the horn mouth, but the horn wall has already curved through 90 degrees before the sound hits the boundary. The reflected sound then has the difficult task of curving back through that 90 degree curve before it can strike the phase plug. Therefore ... no standing wave, only one modest reflection, and very little of the "horn sound" if the compression driver is correctly designed. (Note: there are rectangular horns on the market that are Tractrix-profile in only one dimension...."